Reachable sets for dubins car in control problems: physical visualization

Abstract

The work deals with an application of the 3D-printing to full-size building the reachable sets in control problems. As an example, a simple car model is considered with nonlinear dynamics, three-dimensional phase vector, and scalar control constrained by modulus (Dubins car). Current state of the sytem includes its position in the plane and the velocity heading. The velocity value is given to be constant. The reachable sets are considered “at the terminal instant” and “till the terminal instant”. These sets are nonconvex and their boundaries are not smooth in the whole. Peculiarities of the sets can be better comprehenced being represented in the form of three-dimensional bodies that are built with using the 3D-printing. The sets’ boundaries are presented in the VRML and STL formats. Examples of computation and visualization are given including their 3D-printed copies. Problems are discussed that appear under the 3D-constructing of surfaces with complicated forms.